Dielectrophoretic displays

ABSTRACT

A dielectrophoretic display comprises a substrate having walls defining at least one cavity, the cavity having a viewing surface and a side wall inclined to the viewing surface; a suspending fluid contained within the cavity; a plurality of at least one type of particle suspended within the suspending fluid; and means for applying to the fluid an electric field effective to cause dielectrophoretic movement of the particles to the side wall of the cavity.

REFERENCE TO RELATED APPLICATIONS

This application is a continuation of application Ser. No. 11/799,377,filed May 1, 2007 (Publication No. 2008/0117495), which is acontinuation-in-part of application Ser. No. 10/687,166, filed Oct. 16,2003 (Publication No. 2004/0136048, now U.S. Pat. No. 7,259,744, issuedAug. 21, 2007), which itself claims benefit of Provisional ApplicationSer. No. 60/419,019, filed Oct. 16, 2002. The aforementioned applicationSer. No. 10/687,166 is also a continuation-in-part of application Ser.No. 08/983,404, filed Mar. 26, 1999 (now U.S. Pat. No. 7,106,296), whichis the United States National Phase of International Application No.PCT/US96/12000, filed Jul. 19, 1996, which is itself acontinuation-in-part of application Ser. No. 08/504,896, filed Jul. 20,1995 (now U.S. Pat. No. 6,124,851). The entire disclosure of all theaforementioned applications, and of all U.S. patents and publishedapplications mentioned below, is herein incorporated by reference.

BACKGROUND OF INVENTION

This invention relates to dielectrophoretic displays, and methods foroperating such displays. More specifically, this invention relates todielectrophoretic displays in which solid particles and a suspendingfluid are held within a cavity.

Electrophoretic displays have been the subject of intense research anddevelopment for a number of years. Such displays use a display mediumcomprising a plurality of electrically charged particles suspended in afluid. Electrodes are provided adjacent the display medium so that thecharged particles can be moved through the fluid by applying an electricfield to the medium. In one type of such electrophoretic display, themedium comprises a single type of particle having one opticalcharacteristic in a fluid which has a different optical characteristic.In a second type of such electrophoretic display, the medium containstwo different types of particles differing in at least one opticalcharacteristic and in electrophoretic mobility; the particles may or maynot bear charges of opposite polarity. The optical characteristic whichis varied is typically color visible to the human eye, but may,alternatively or in addition, be any one of more of reflectivity,retroreflectivity, luminescence, fluorescence, phosphorescence, or (inthe case of displays intended for machine reading) color in the broadersense of meaning a difference in absorption or reflectance atnon-visible wavelengths.

Electrophoretic displays can be divided into two main types, namelyunencapsulated and encapsulated displays. In an unencapsulatedelectrophoretic display, the electrophoretic medium is present as a bulkliquid, typically in the form of a flat film of the liquid presentbetween two parallel, spaced electrodes. Such unencapsulated displaystypically have problems with their long-term image quality which haveprevented their widespread usage. For example, particles that make upsuch electrophoretic displays tend to cluster and settle, resulting ininadequate service-life for these displays.

An encapsulated, electrophoretic display differs from an unencapsulateddisplay in that the particle-containing fluid is not present as a bulkliquid but instead is confined within the walls of a large number ofsmall capsules. Encapsulated displays typically do not suffer from theclustering and settling failure mode of traditional electrophoreticdevices and provides further advantages, such as the ability to print orcoat the display on a wide variety of flexible and rigid substrates.

For further details regarding encapsulated electrophoretic displays, thereader is referred to U.S. Pat. Nos. 5,930,026; 5,961,804; 6,017,584;6,067,185; 6,118,426; 6,120,588; 6,120,839; 6,124,851; 6,130,773;6,130,774; 6,172,798; 6,177,921; 6,232,950; 6,249,271; 6,252,564;6,262,706; 6,262,833; 6,300,932; 6,312,304; 6,312,971; 6,323,989;6,327,072; 6,376,828; 6,377,387; 6,392,785; 6,392,786; 6,413,790;6,422,687; 6,445,374; 6,445,489; 6,459,418; 6,473,072; 6,480,182;6,498,114; 6,504,524; 6,506,438; 6,512,354; 6,515,649; 6,518,949;6,521,489; 6,531,997; 6,535,197; 6,538,801; 6,545,291; and 6,580,545;and U.S. Patent Applications Publication Nos. 2002/0019081;2002/0021270; 2002/0053900; 2002/0060321; 2002/0063661; 2002/0063677;2002/0090980; 2002/0106847; 2002/0113770; 2002/0130832; 2002/0131147;2002/0145792; 2002/0171910; 2002/0180687; 2002/0180688; 2002/0185378;2003/0011560; 2003/0011867; 2003/0011868; 2003/0020844; 2003/0025855;2003/0034949; 2003/0038755; 2003/0053189; 2003/0076573; 2003/0096113;2003/0102858; 2003/0132908; 2003/0137521; 2003/0137717; and2003/0151702; and International Applications Publication Nos. WO99/67678; WO 00/05704; WO 00/38000; WO 00/38001; WO 00/36560; WO00/67110; WO 00/67327; WO 01/07961; and WO 01/08241. All of thesepatents and applications are in the name of, or assigned to, theMassachusetts Institute of Technology (MIT) or E Ink Corporation.

Many of the aforementioned patents and applications recognize that thewalls surrounding the discrete microcapsules in an encapsulatedelectrophoretic medium could be replaced by a continuous phase, thusproducing a so-called “polymer-dispersed” electrophoretic display inwhich the electrophoretic medium comprises a plurality of discretedroplets of an electrophoretic fluid and a continuous phase of apolymeric material, and that the discrete droplets of electrophoreticfluid within such a polymer-dispersed electrophoretic display may beregarded as capsules or microcapsules even though no discrete capsulemembrane is associated with each individual droplet; see for example,U.S. Pat. No. 6,392,786, at column 6, lines 44-63. See also theaforementioned U.S. Patent Application Publication No. 2002/0131147, andthe corresponding International Application PCT/US02/06393 (PublicationNo. WO 02/075443). Accordingly, for purposes of the present application,such polymer-dispersed electrophoretic media are regarded as sub-speciesof encapsulated electrophoretic media.

A related type of electrophoretic display is a so-called “microcellelectrophoretic display”, sometimes also called a “microcup”electrophoretic display. In a microcell electrophoretic display, thecharged particles and the suspending fluid are not encapsulated withinmicrocapsules but instead are retained within a plurality of cavitiesformed within a carrier medium (or substrate), typically a polymericfilm. See, for example, International Applications Publication No. WO02/01281, and published US Application No. 2002/0075556, both assignedto Sipix Imaging, Inc.

Hereinafter, the term “microcavity electrophoretic display” will be usedto cover both encapsulated and microcell electrophoretic displays.

One of the problems with electrophoretic displays is the limited rangeof colors which each pixel of the display can produce. The prior artdescribes two main types of electrophoretic media. One type comprises asingle type of electrically charged particle in a colored medium. Thistype of medium is only capable of producing two colors at each pixel;either the color of the particles or the color of the medium is seen.The second type of medium comprises two different types of electricallycharged particles in an essentially uncolored medium; the two types ofparticles may differ in polarity of electric charge or have charges ofthe same polarity but differ in electrophoretic mobility. Again, thistype of medium is only capable of producing two colors at each pixel,namely the colors of the two types of particles.

One approach to expanding the limited range of colors available fromconventional electrophoretic displays is to place an array of coloredfilters over the pixels of the display. For example, consider the effecton a display comprising white particles in a black fluid of placing anarray of color filters (say red, green and blue) over the individualpixels of the display. Moving the white particles adjacent the viewingsurface of a pixel covered with a red filter would color that pixel red,whereas moving the white particles of the same pixel adjacent the rearsurface of the display would render the pixel black. The main problemwith this approach to generating color is that the brightness of thedisplay is limited by the pixelation of the color filter. For example,if a red color is desired, the pixels covered by red filters are set toappear red. whereas the pixels covered by green and blue filters are setto appear dark, so that only a fraction of the display surface has thedesired color while the remaining portion is dark, thus limiting thebrightness of any color obtained. A reflective display that was capableof three optical states (black, white and color or black, white andtransparent) would significant advantages in image quality, cost andease of manufacture.

Conventional electrophoretic displays rely upon movement of electricallycharged particles in an electric field under electrostatic forces; theparticles move along the lines of force of the electric field. However,it is known that objects can be moved by dielectrophoretic forces, thatis to say that dipoles induced in the objects by a non-uniform electricfield cause the particles to move towards regions of higher fieldstrength. See, for example, U.S. Pat. No. 4,418,346 to Batchelder whichdescribes an apparatus for providing a dielectrophoretic display ofvisual information. In this apparatus, a “bubble” of a fluid is movedthrough a second, immiscible fluid in a stepwise manner by applyingvoltages to closely spaced electrodes, the bubble being visible againsta visually contrasting background. Visual information is conveyed by theposition of the bubble relative to the background. The patent suggeststhat a simple one-dimensional display of this type might represent thelevel of an analog signal by the position of the bubble. However, sincethe movement involved is that of a bubble against a contrastingbackground, such an apparatus does not appear capable of displaying anarbitrary image.

It has now been realized that using a microcavity electrophoretic mediumin a dielectrophoretic display greatly simplifies the problem ofgenerating the heterogeneous electric field required by such a display,since differences between the dielectric constant and/or conductivitybetween the suspending fluid and the material surrounding the suspendingfluid (such as a polymeric binder in which the capsules are embedded, asdescribed in many of the aforementioned E Ink and MIT patents andpublications, or the substrate in which the cavities of a microcellelectrophoretic display are formed) will result in a heterogeneouselectric field which can be used to move the particles within thesuspending fluid against the side walls of the cavities, therebyproviding the display with a substantially transparent state.

SUMMARY OF THE INVENTION

Accordingly, this invention provides a dielectrophoretic displaycomprising:

a substrate having walls defining at least one cavity, the cavity havinga viewing surface and a side wall inclined to the viewing surface;

a suspending fluid contained within the cavity;

a plurality of at least one type of particle suspended within thesuspending fluid; and

means for applying to the fluid an electric field effective to causedielectrophoretic movement of the particles to the side wall of thecavity.

This invention also provides a process for operating a dielectrophoreticdisplay, the process comprising:

providing a substrate having walls defining at least one cavity, thecavity having a viewing surface and a side wall inclined to the viewingsurface; a suspending fluid contained within the cavity; and a pluralityof at least one type of particle suspended within the suspending fluid;and

applying to the fluid an electric field effective to causedielectrophoretic movement of the particles to the side wall of thecavity.

In the dielectrophoretic display of the present invention, thesuspending fluid may be substantially uncolored, and have suspendedtherein only a single type of particle.

At least some of the at least one type of particle may be electricallycharged, and in one form of a display containing such electricallycharged particles, the suspending fluid may have suspended therein afirst type of particle having a first optical characteristic and a firstelectrophoretic mobility, and a second type of particle having a secondoptical characteristic different from the first optical characteristicand a second electrophoretic mobility different from the firstelectrophoretic mobility. The first and second electrophoreticmobilities may differ in sign, so that the first and second types ofparticles move in opposed directions in an electric field, and thesuspending fluid may be substantially uncolored. This type of displaymay further comprise a backing member disposed on the opposed side ofthe cavity from the viewing surface, at least part of the backing memberhaving a third optical characteristic different from the first andsecond optical characteristics. The backing member may comprise areashaving third and fourth optical characteristics different from eachother and from the first and second optical characteristics. Inpreferred forms of such a display, the backing member comprises areashaving red, green and blue or yellow, cyan and magenta colors, and thefirst and second optical characteristics may comprise black and whitecolors.

In the dielectrophoretic display of the present invention, the cavitymay have a non-circular cross-section, preferably a polygonalcross-section, as seen from the viewing surface. The at least one typeof particle may be formed from an electrically conductive material, forexample a metal, carbon black or a doped semiconductor.

As already indicated, in the dielectrophoretic display of the presentinvention, the substrate may comprises at least one capsule wall(typically a deformable wall) so that the dielectrophoretic displaycomprises at least one capsule. For reasons explained in theaforementioned 2003/0137717, the capsules are preferably arranged in asingle layer. Alternatively, the substrate may comprise a continuousphase surrounding a plurality of discrete droplets of the suspendingfluid having the at least one type of particle suspended therein (i.e.,the display may be of the polymer-dispersed type), or may comprises asubstantially rigid material having the at least one cavity formedtherein, the substrate further comprising at least one cover memberclosing the at least one cavity, so that the display is of the microcelltype.

In the process of the present invention, the electric field may be analternating electric field. When the display is of the type in which atleast some of the at least one type of particle are electricallycharged, and the suspending fluid has suspended therein a first type ofparticle having a first optical characteristic and a firstelectrophoretic mobility, and a second type of particle having a secondoptical characteristic different from the first optical characteristicand a second electrophoretic mobility different from the firstelectrophoretic mobility, with the first and second electrophoreticmobilities differing in sign, so that the first and second types ofparticles move in opposed directions in an electric field, the processmay further comprise:

applying an electric field of a first polarity to the cavity, therebycausing the first type of particles to approach the viewing surface andthe cavity to display the first optical characteristic at the viewingsurface; and

applying an electric field of a polarity opposite to the first polarityto the cavity, thereby causing the second type of particles to approachthe viewing surface and the cavity to display the second opticalcharacteristic at the viewing surface.

This invention also provides a dielectrophoretic display comprising:

-   -   a substrate having walls defining at least one cavity, the        cavity having a viewing surface and a side wall inclined to the        viewing surface;    -   a fluid contained within the cavity;    -   a plurality of at least one type of electrically charged        particle within the fluid, the particles having a first optical        characteristic;    -   a backing member disposed on the opposed side of the cavity from        the viewing surface, at least part of the backing member having        a second optical characteristic different from the first optical        characteristics, the backing member being light-transmissive;        and    -   means for applying to the substrate an electric field effective        to cause dielectrophoretic movement of the particles to the side        wall of the cavity.

In one form of such a dielectrophoretic display, the fluid issubstantially uncolored, and has therein only a single type of particle.The cavity may have a non-circular (and preferably polygonal)cross-section as seen from the viewing surface. The single type ofparticle may be formed from an electrically conductive material, forexample a metal or carbon black. Alternatively, the single type ofparticle may be formed from a doped semiconductor.

The substrate may comprise at least one capsule wall so that thedielectrophoretic display comprises at least one capsule. The displaymay comprise a plurality of capsules, the capsules being arranged in asingle layer. Alternatively, the substrate may comprise a continuousphase surrounding a plurality of discrete droplets of the fluid havingthe particles therein. In another form of such a dielectrophoreticdisplay, the substrate comprises a substantially rigid material havingthe at least one cavity formed therein, the substrate further comprisingat least one cover member closing the at least one cavity.

The dielectrophoretic display may be arranged to have light projected onto a surface on the opposed side of the dielectrophoretic display fromthe viewing surface. The invention extends to a variable transmissionwindow comprising a dielectrophoretic display of the invention.

This invention also provides a process for operating a dielectrophoreticdisplay, the process comprising:

-   -   providing a substrate having walls defining at least one cavity,        the cavity having a viewing surface and a side wall inclined to        the viewing surface, a fluid contained within the cavity; and a        plurality of at least one type of electrically charged particle        suspended within the suspending fluid, the particles having a        first optical characteristic; and a backing member disposed on        the opposed side of the cavity from the viewing surface, at        least part of the backing member having a second optical        characteristic different from the first optical characteristic,        the backing member being light-transmissive; and    -   applying to the substrate an electric field effective to cause        dielectrophoretic movement of the particles to the side wall of        the cavity.

In this process, the electric field may be an alternating electricfield. The fluid may be substantially uncolored and have therein only asingle type of particle. This single type of particle may be formed froman electrically conductive material, for example a metal or carbonblack. Alternatively, the single type of particle may be formed from adoped semiconductor. The substrate may comprise at least one capsulewall so that the dielectrophoretic display comprises at least onecapsule. The display may comprise a plurality of capsules, the capsulesbeing arranged in a single layer. Alternatively, the substrate maycomprise a continuous phase surrounding a plurality of discrete dropletsof the fluid having the particles therein. In another form of such adielectrophoretic display, the substrate comprises a substantially rigidmaterial having the at least one cavity formed therein, the substratefurther comprising at least one cover member closing the at least onecavity.

This invention also provides an electronically addressable displaycomprising a microencapsulated display medium including a first specieshaving a higher dielectric constant and a second species having a lowerdielectric constant; and electrodes disposed adjacent the display mediumfor selectively creating regions of higher and lower electric field; andwherein the first species moves toward the region of higher electricfield.

In such an electronically addressable display, the display medium maycomprise a bichromal microsphere having a first hemisphere and a secondhemisphere differing in dielectric constants, wherein the first speciesof higher dielectric constant comprises the first hemisphere and thesecond species of lower dielectric constant comprises the secondhemisphere. Alternatively, the display medium may comprise a firstspecies of colored particles having a higher dielectric constant and asecond species of colored particles having a lower dielectric constant.The first species may have a dielectric constant that is permanentlyhigher than that of the second species. The first species may move intranslational migration.

This invention also provides a process for operating a dielectrophoreticdisplay, the process comprising:

-   -   providing a substrate having walls defining at least one cavity,        the cavity having a viewing surface and a side wall inclined to        the viewing surface, a fluid contained within the cavity; and a        plurality of solid particles within the fluid, the particles        having a dielectric constant higher than the dielectric constant        of the fluid; and    -   applying to the substrate a non-homogeneous electric field, the        electric field being greater adjacent the side wall than in the        center of the cavity, thereby causing the particles to move to        the side wall of the cavity.

This invention also provides a process for operating a dielectrophoreticdisplay, the process comprising:

-   -   providing a substrate having walls defining at least one cavity,        the cavity having a viewing surface and a side wall inclined to        the viewing surface, a fluid contained within the cavity; and a        plurality of solid particles within the fluid, the particles        having a dielectric constant lower than the dielectric constant        of the fluid; and    -   applying to the substrate a non-homogeneous electric field, the        electric field being smaller adjacent the side wall than in the        center of the cavity, thereby causing the particles to move to        the side wall of the cavity.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 of the accompanying drawings is a schematic section showing awhite opaque state of a dielectrophoretic display of the presentinvention.

FIG. 2 is a schematic section similar to FIG. 1 but showing a blackopaque state of the display shown in FIG. 1.

FIG. 3 is a schematic section similar to FIGS. 1 and 2 but showing atransparent state of the display shown in FIGS. 1 and 2.

FIGS. 4 to 6 are top plan views through the viewing surface of anexperimental display in the states corresponding to FIGS. 1 to 3respectively.

FIGS. 7 and 8 illustrate the transition from the white optical state ofthe display shown in FIG. 4 to the transparent state shown in FIG. 6.

FIGS. 9 to 11 are schematic sections through a microcell display of thepresent invention in states corresponding to those of FIGS. 1 to 3respectively.

FIGS. 12A to 12D are schematic details of dielectrophoretic switchedelectronically addressed contrast media of the present invention.

FIG. 13 illustrates the forces acting on a dipole in a non-uniformelectric field.

FIG. 14 is a graph illustrating the variation of the contrast functionwith the ratio of the dielectric constants of the particle and the fluidfor an insulating particle in an insulating fluid.

DETAILED DESCRIPTION

As already mentioned, in one aspect this invention provides adielectrophoretic display comprising a substrate having walls definingat least one cavity, the cavity having a viewing surface and a side wallinclined to the viewing surface; a suspending fluid contained within thecavity; a plurality of at least one type of particle suspended withinthe suspending fluid; and means for applying to the fluid an electricfield effective to cause dielectrophoretic movement of the particles tothe side wall of the cavity.

References to “viewing surface” and “side wall” herein do not imply thatthese surfaces are perpendicular to each other, though a substantiallyperpendicular arrangement of the two surfaces is preferred, since whenthe particles are disposed adjacent the side wall of the cavity, such aperpendicular arrangement minimizes the area of the viewing surfaceoccupied by the particles, and hence permits the maximum amount of lightto pass through the cavity. The side wall or walls of the cavity alsoneed not be planar; for example, an encapsulated display of the presentinvention may use capsules as described in the aforementioned U.S. Pat.No. 6,067,185 having the form of “flattened spheres” (i.e., oblateellipsoids) with curved side walls.

In this display, it is necessary that there be a difference between thedielectric constant and/or conductivity of the suspending fluid and thatof the substrate to provide the heterogeneous electric field necessaryfor dielectrophoresis. Desirably, this difference should be made aslarge as possible. It may also be advantageous to use a capsule whichhas a non-circular, and preferably polygonal, cross-sectionperpendicular to the direction of the applied electric field sincesharply curved regions or corners of the capsule produce increased fieldheterogeneity and thus assist the dielectrophoretic movement of theparticles.

Those skilled in the technology of electrophoretic displays willappreciate that both electrically neutral and electrically chargedparticles can be moved by dielectrophoresis, since dielectrophoreticmovement is dependent upon dipoles induced in the particles by theelectric field and not upon any pre-existing charge on the particles.However, it appears advantageous to use electrically charged particlesin the apparatus and process of the present invention since once theparticles have been moved to the side wall of the capsule bydielectrophoresis, it appears desirable to use normal electrophoreticmovement of the particles to disperse them; it will be appreciated thatsince the heterogeneity of the electric field in an encapsulated displayis due to differences between the properties of the suspending fluid onthe one hand and the capsule wall and surrounding material on the other,there will normally be no way of reversing the high field and low fieldregions in a manner similar to that used in the Batchelder apparatus, sothat if the particle movement caused by dielectrophoresis is to bereversed, some applied force other than dielectrophoresis must be used.

If electrically charged particles are used in the present apparatus andprocess, the particles are of course subject to both electrophoretic anddielectrophoretic forces when an electric field is applied. Typically,electrophoretic movement of particles will be much more rapid thandielectrophoretic, so that to ensure that the desired dielectrophoreticmovement is not subject to interference from electrophoretic movement,it is desirable to reverse the electric field at intervals; provided thefield is applied for the same amount time in each direction, theelectrophoretic movements will sum to zero, since electrophoreticmovement is polarity-sensitive, whereas the dielectrophoretic movementswill not sum to zero since dielectrophoretic movement ispolarity-independent.

The dielectrophoretic movement of the particles in the apparatus andprocess of the present invention is affected by the material from whichthe particles are formed, and the size and shape of the particles. Sincedielectrophoresis depends upon the induction of dipoles within theparticles, it is desirable to use particles which are highlypolarizable, especially conductive particles such as metals. Forexample, aluminum particles may be used in the present invention. It hasbeen observed experimentally that carbon black particles, which have areasonably high conductivity, have substantially greaterdielectrophoretic mobility than substantially non-conductive titaniaparticles. The particles may also be formed from a doped semiconductor;the type of doping is not critical provided that the particles havesufficient conductivity, but most undoped semiconductors have too low aconductivity to have high dielectrophoretic mobility.

The induced dipole, and hence the dielectrophoretic movement of theparticles, is also affected by the size and shape of the particles.Since a large particle allows greater separation between the poles of adipole than a smaller particle, increasing the size of the particleswill increase dielectrophoretic mobility, although of course theparticles should not be made so large as to readily visible when theylie adjacent the side wall of the capsule. For similar reasons, elongateparticles, especially needle-shaped particles, will tend to have ahigher dielectrophoretic mobility than spherical particles of the samevolume. Anisotropically shaped particles may also be useful in thepresent invention.

There are two main variations of the apparatus and process of thepresent invention. In the first variation, the cavity contains only asingle type of particle in an uncolored suspending fluid. This capsulecan be switched between an “opaque” state, in which the particles aredispersed throughout the suspending fluid, and a “transparent” state, inwhich the particles are moved to a side wall of the capsule so thatlight can pass through the uncolored suspending fluid. The transparentstate need not appear transparent to a viewer; as illustrated in thedrawings and as described in more detail below, a reflector or filterhaving a color different from that of the particles may be placed on theopposed side of the capsule from the viewing surface thereof, so that inthe transparent state a viewer sees the color of the reflector orfilter; in the opaque state the color of the reflector or filter is ofcourse hidden by the dispersed particles.

In the second variation, the capsules contain two different types ofparticles differing in at least one optical characteristic and inelectrophoretic mobility and a suspending fluid which may be colored oruncolored. This capsule can be switched among three states, namely afirst opaque state, in which the first type of particles are visible, asecond opaque state, in which the second type of particles are visible,and a “transparent” state, in which both types of particles are moved toa side wall of the capsule by dielectrophoresis and the color of thesuspending fluid is visible; if, as will typically be the case, thesuspending fluid is uncolored, the transparent state is actuallytransparent and may be used to display the color of a reflector orfilter disposed on the opposed side of the capsule from the viewingsurface thereof, as previously described.

It will be appreciated that, provided that the desired color can be seenwhen a display of the present invention is in a transparent state, thelocation of the colored material is essentially irrelevant. Thus,although reference has been made above to a reflector or filter, it isnot essential that this reflector or filter be a discrete integer, andcolor could be provided in any convenient location. Thus, for example,the colored reflector or filter could be provided by coloring (a) thesubstrate itself, for example the polymeric film used in a microcellform of the present display; (b) a material associated with thesubstrate, for example a polymeric binder used to retain capsules in acoherent layer in an encapsulated display of the invention, or alamination adhesive layer used to secure the dielectrophoretic layer toa backplane; or (c) the pixel electrodes or another component of abackplane used to drive the display. In principle, in an encapsulateddisplay color could be provided by dyeing the capsule walls themselves,but this does have the disadvantage that in an opaque state of a pixelthe color in the portion of the capsule adjacent the viewing surfacewill affect the color seen at that surface when the pixel is in anopaque state. In some cases, the resultant color shift may beacceptable, or may be minimized, for example by using particles whichhave a color complementary to that of the color caused by the capsulewall. In other cases, color may be provided only on the parts of thecapsule wall lying on the opposed side of the capsule to the viewingsurface, for example by providing a radiation-sensitive color-formingmaterial in the capsule wall and then exposing this color-formingmaterial to radiation effective to bring about the formation of color,this radiation being directed on to the capsule from the side of thedisplay opposite to the viewing surface.

Color could also be provided from a source separate from the displayitself. For example, if a display of the present invention is arrangedto operate as a light valve and backlit by projecting light on to asurface on the opposed side of the display from the viewing surface,color could be provided by imaging an appropriate color filter on to therear surface of the display.

Except in cases where it is essential that the colored member be lighttransmissive, the color may be provided either by dyes or pigments,although the latter are generally preferred since they are typicallymore stable against prolonged exposure to radiation, and thus tend toprovide displays with longer operating lifetimes.

As already indicated, no special electrode configurations are requiredin the display and process of the present invention; the invention canbe practiced with simple parallel electrodes on opposed sides of thecavity; for example, a multi-pixel display of the invention using atleast one cavity per pixel could have the conventional electrodeconfiguration of a single pixel electrode for each pixel on one side ofthe cavities and a single common electrode extending across all thepixels on the opposed side of the cavities. However, this invention doesnot exclude the possibility that the electrodes might be shaped toenhance the dielectrophoretic effect. It may also be useful to useso-called “z-axis adhesives” (i.e., adhesives having a substantiallygreater conductivity parallel to the thickness of a layer of adhesivethan in the plane of this layer) between one or both of the electrodesand the cavities cf. copending Application Ser. No. 60/319,934, filedFeb. 11, 2003, the entire disclosure of which is herein incorporated byreference. In addition, as discussed in detail below with reference tothe drawings, in some embodiments of the invention it may beadvantageous to provide auxiliary electrodes to assist in redispersingthe particles in the suspending fluid after the particles have be drivento the side walls by dielectrophoresis.

As already mentioned, there are three principal types ofdielectrophoretic displays of the present invention. The first type isthe “classical” encapsulated electrophoretic type as described in theaforementioned E Ink and MIT patents and applications. In this type ofdisplay, the substrate has the form of at least one capsule wall, whichis typically deformable, and formed by depositing a film-formingmaterial around a droplet containing the suspending fluid and thedielectrophoretic particles. The second type is the polymer-dispersedelectrophoretic type in which the substrate comprises a continuous phasesurrounding a plurality of discrete droplets of the suspending fluid.Full details regarding the preparation of this type of display are givenin the aforementioned 2002/0131147. The third type is the microcelldisplay, in which a plurality of cavities or recesses are formed in asubstrate, filled with the suspending fluid and particles and thensealed, either by lamination a cover sheet over the recesses or bypolymerizing a polymerizable species also present in the suspendingfluid.

The first dielectrophoretic display (generally designated 100) of theinvention shown in FIGS. 1 to 3 comprises an encapsulateddielectrophoretic medium (generally designated 102) comprising aplurality of capsules 104 (only one of which is shown in FIGS. 1 to 3),each of which contains a suspending liquid 106 and dispersed therein aplurality of a first type of particle 108, which for purposes ofillustration will be assumed to be black. The particles 108 areelectrophoretically mobile and may be formed of carbon black. In thefollowing description, it will be assumed that the particles 108 arepositively charged, although of course negatively charged particlescould also be used if desired. Also suspended in the suspending liquid106 is a plurality of a second type of particle 110, which iselectrophoretically mobile and negatively charged, and may be formed oftitania. (The triangular shape of the particles 108, and the circularshape of the particles 110 are used purely to way of illustration toenable the various types of particles to be distinguished easily in theaccompanying drawings, and in no way correspond to the physical forms ofthe actual particles, which are typically substantially spherical.However, we do not exclude the use of non-spherical particles in thepresent displays.) The display 100 further comprises a common,transparent front electrode 112, which forms a viewing surface throughwhich an observer views the display 100, and a plurality of discreterear electrodes 114, each of which defines one pixel of the display 100(only one rear electrode 114 is shown in FIGS. 1 to 3). (The frontelectrode 112 is typically provided on a support member which alsoprovides mechanical protection for the display 100 but for simplicitythis support member is omitted from FIGS. 1 to 3.) For ease ofillustration and comprehension, FIGS. 1 to 3 show only a singlemicrocapsule forming the pixel defined by rear electrode 114, althoughin practice a large number (20 or more) microcapsules are normally usedfor each pixel. The rear electrodes 114 are mounted upon a substrate116, which contains areas of differing color, as described in moredetail below with reference to FIGS. 4 to 8.

Typically the liquid 106 is uncolored (i.e., essentially transparent),although some color may be present therein to adjust the opticalproperties of the various states of the display. FIG. 1 shows thedisplay 100 with the front electrode 112 positively charged relative tothe rear electrode 114 of the illustrated pixel. The positively chargedparticles 108 are held electrostatically adjacent the rear electrode114, while the negatively charged particles 110 are heldelectrostatically against the front electrode 112. Accordingly, anobserver viewing the display 100 through the front electrode 112 sees awhite pixel, since the white particles 110 are visible and hide theblack particles 108.

FIG. 2 shows the display 100 with the front electrode 112 negativelycharged relative to the rear electrode 114 of the illustrated pixel. Thepositively charged particles 108 are now electrostatically attracted tothe negative front electrode 112, while the negatively charged particles110 are electrostatically attracted to the positive rear electrode 114.Accordingly, the particles 108 move adjacent the front electrode 112,and the pixel displays the black color of the particles 108, which hidethe white particles 110.

FIG. 3 shows the display 100 after application of an alternatingelectric field between the front and rear electrodes 112 and 114respectively. The application of the alternating electric field causesdielectrophoretic movement of both types of particles 108 and 110 to theside walls of the capsule 104, thus leaving the major portion of thearea of the capsule 104 essentially transparent. Accordingly, the pixeldisplays the color of the substrate 116.

To redisperse the particles 108 and 110 uniformly throughout thesuspending liquid 106 from their positions shown in FIG. 3, a series ofshort direct current voltages of alternating polarity is applied betweenthe front and rear electrodes 112 and 114, thereby causing the particles108 and 110 to oscillate within the suspending liquid 106; thisoscillation causes the particles 108 and 110 to gradually redispersethroughout the liquid 106. Application of a longer direct current pulseof appropriate polarity will then cause the pixel to assume the stateshown in FIG. 1 or 2 depending upon the polarity of the longer pulse.

In FIGS. 1 to 3, the capsules 104 are illustrated as being ofsubstantially prismatic form, having a width (parallel to the planes ofthe electrodes) significantly greater than their height (perpendicularto these planes). This prismatic shape of the capsules 104 is deliberatesince it provides the capsules with side walls which extend essentiallyperpendicular to the viewing surface of the display, thus minimizing theproportion of the area of the capsule 104 which is occupied by theparticles 108 and 110 in the transparent state shown in FIG. 3. Also, ifthe capsules 104 were essentially spherical, in the black state shown inFIG. 2, the particles 108 would tend to gather in the highest part ofthe capsule, in a limited area centered directly above the center of thecapsule. The color seen by the observer would then be essentially theaverage of this central black area and a white or colored annulussurrounding this central area, where either the white particles 110 orthe substrate 116 would be visible. Thus, even in this supposedly blackstate, the observer would see a grayish color rather than a pure black,and the contrast between the two extreme optical states of the pixelwould be correspondingly limited. In contrast, with the prismatic formof microcapsule shown in FIGS. 1 and 2, the particles 108 coveressentially the entire cross-section of the capsule so that no, or atleast very little, white or other colored area is visible, and thecontrast between the extreme optical states of the capsule is enhanced.For further discussion on this point, and on the desirability ofachieving close-packing of the capsules within the electrophoreticlayer, the reader is referred to the aforementioned U.S. Pat. No.6,067,185. Also, as described in the aforementioned E Ink and MITpatents and applications, to provide mechanical integrity to thedielectrophoretic medium, the capsules 104 are normally embedded withina solid binder, but this binder is omitted from FIGS. 1 to 3 for ease ofillustration.

FIGS. 4, 5 and 6 of the accompanying drawings illustrate the whiteopaque, black opaque and transparent optical states of an experimentaldisplay of the present invention substantially as described above withreference to FIGS. 1 to 3 and comprising a plurality of capsules, eachof which contains carbon black and white titania particles bearingcharges of opposite polarity in a colorless suspending fluid. Thedisplay was prepared substantially as described in the aforementioned2003/0137717 by encapsulating a hydrocarbon suspending fluid containingthe carbon black and titania particles in a gelatin/acacia capsule wall,mixing the resultant capsules with a polymeric binder, coating thecapsule/binder mixture on to an indium tin oxide (ITO) coated surface ofa polymeric film to provide a single layer of capsules covering thefilm, and laminating the resultant film to a backplane. For purposes ofillustration, the display shown in FIGS. 4, 5 and 6 was formed as asingle pixel with the transparent front electrode forming the viewingsurface of the display, and the backplane (actually a single rearelectrode) disposed adjacent a multicolored reflector.

FIG. 4 shows the display in its first, white opaque state correspondingto that of FIG. 1, with the white particles moved by electrophoresis andlying adjacent the viewing surface of the display, so that the whiteparticles hide both the black particles and the multicolored reflector,and the display appears white. Similarly, FIG. 5 shows the display inits second, black opaque state corresponding to that of FIG. 2, with theblack particles moved by electrophoresis and lying adjacent the viewingsurface of the display, so that the black particles hide both the whiteparticles and the multicolored reflector, and the display appears black.FIG. 6 shows the display in a transparent state corresponding to that ofFIG. 3 caused by applying a square wave with a frequency of 60 Hz and anamplitude of 90V until no further change was visible in the display(approximately 150 seconds). The application of this square wave causedboth the black and white particles to move dielectrophoretically to theside walls of the capsules, thus causing the multicolored reflector tobe visible through the uncolored suspending fluid. Thus, a display ofthe type shown in FIGS. 1 to 6 can display three different colors, whicheases the problems of building a full color electro-optic display.

FIGS. 7 and 8 illustrate the transition from the white opaque stateshown in FIG. 4 to the transparent state shown in FIG. 6; FIG. 7 showsthe display after application of the aforementioned square wave for 10seconds, while FIG. 8 shows the display after application of the squarewave for 30 seconds. It will be seen from FIGS. 6, 7 and 8 thatdevelopment of the transparent state occurs gradually as more and moreparticles are moved to the side walls of the capsules. In FIG. 7, themulticolored reflector is just becoming visible, while in FIG. 8 thisreflector is more visible but much less clear than in the finaltransparent state shown in FIG. 6.

FIGS. 9 to 11 show schematic sections, similar to those of FIGS. 1 to 3respectively, of one pixel of a microcell display (generally designated900) of the present invention. The microcell display 900 usesessentially the same dielectrophoretic medium, comprising a suspendingliquid 106 with carbon black particles 108 and white titania particlessuspended therein, as the encapsulated display 100 shown in FIGS. 1 to3; however, the form of substrate used in the display 900 differssubstantially from that of the display 100. In the display 900, thesubstrate comprises a base member 120 and a plurality of side walls 122extending perpendicular to the base member 120 and forming a pluralityof microcells in which are confined the liquid 106 and the particles 108and 110. The lower faces (as illustrated in FIGS. 9 to 11) of themicrocells are closed by closure walls 124, which are formed byradiation polymerization of a polymerizable species originally presentin the liquid 106; see the aforementioned International ApplicationPublication No. WO 02/01281, and published US Application No.2002/0075556. The display 900 further comprises a front electrode 112, arear or pixel electrode 114 and a colored substrate 116 all of which areessentially identical to the corresponding integers in FIG. 1. (In thesame way as in FIGS. 1 to 3, for simplicity FIGS. 9 to 11 are drawn asif there is only a single microcell to the pixel defined by theelectrode 114 although in practice a single pixel may comprise multiplemicrocells.) The display 900 also comprises auxiliary electrodesembedded within the side walls 122 and a protective layer 126 coveringthe front electrode 112.

As shown in FIGS. 9 to 11, the microcell display 900 operates in amanner very similar to the encapsulated display 100 shown in FIGS. 1 to3. FIG. 9 shows the display 900 with the front electrode 112 positivelycharged relative to the rear electrode 114 of the illustrated pixel. Thepositively charged particles 108 are held electrostatically adjacent therear electrode 114, while the negatively charged particles 110 are heldelectrostatically against the front electrode 112. Accordingly, anobserver viewing the display 100 through the front electrode 112 sees awhite pixel, since the white particles 110 are visible and hide theblack particles 108.

FIG. 10 shows the display 900 with the front electrode 112 negativelycharged relative to the rear electrode 114 of the illustrated pixel. Thepositively charged particles 108 are now electrostatically attracted tothe negative front electrode 112, while the negatively charged particles110 are electrostatically attracted to the positive rear electrode 114.Accordingly, the particles 108 move adjacent the front electrode 112,and the pixel displays the black color of the particles 108, which hidethe white particles 110.

FIG. 11 shows the display 900 after application of an alternatingelectric field between the front and rear electrodes 112 and 114respectively. The application of the alternating electric field causesdielectrophoretic movement of both types of particles 108 and 110 to theside walls of the microcell, thus leaving the major portion of the areaof the microcell essentially transparent. Accordingly, the pixeldisplays the color of the substrate 116.

Redispersion of the particles 108 and 110 from the transparent state ofthe display 900 shown in FIG. 11 may be effected in the same way asdescribed above for the display 100. However, the auxiliary electrodes126 are provided to assist in such redispersion. The auxiliaryelectrodes run the full width of the display (which is assumed to beperpendicular to the plane of FIGS. 9 to 11), i.e., each auxiliaryelectrode is associated with a full row of microcells, and the auxiliaryelectrodes are connected to a voltage source which, when activated,applies voltages of opposed polarities to alternate auxiliary electrodes126. By applying a series of voltage pulses of alternating polarity tothe auxiliary electrodes 126, an electric field is created in theleft-right direction in FIGS. 9 to 11, which greatly assists isredispersing all the particles 108 and 110 throughout the displayuniformly within the liquid 106. Voltage pulses of alternating polaritymay also be applied to the electrodes 112 and 114 as previouslydescribed to further assist in redispersing the particles 108 and 110.

FIGS. 12A-12D illustrate electronically addressable contrast media(i.e., dielectrophoretic displays) of the present invention which areaddressed by electrodes disposed only on the rear surface (i.e., thesurface remote from the viewing surface) of the display. In thesedisplays, as described in Application Ser. No. 60/022,222 (see also U.S.Pat. No. 6,120,588, which issued on application Ser. No. 08/935,800,filed Sep. 23, 1997, which is effect the completion of Application Ser.No. 60/022,222), the dielectrophoretic effect is employed to cause aspecies (particle) of higher dielectric constant to move to a region ofhigher field strength.

In FIGS. 12A and 12B, a capsule 420 contains a non-colored dye solventcomplex 503. a pair of electrodes 502 are disposed adjacent the rear(non-viewing) surface of the capsule 420. (In all of FIGS. 12A-12D, asin FIGS. 1-3 and 9-11, it is assumed that the display is to be viewedfrom above as illustrated.) The complex 503 is stable when no field isapplied across the pair of electrodes 502. However, when an electricfield 506 is applied across the pair of electrodes 502, as illustratedin FIG. 12B, the complex 503 dissociates into a colored dye component504 and a solvent component 505, with the dye component 504 moving awayfrom the electrodes 502 towards a region of lower electric field.

FIGS. 12C and 12D illustrate electronically addressable contrast mediasimilar to that illustrated in FIGS. 12A and 12B but using two pairs ofstacked electrodes 502, 507 in place of the single pair of electrodes502 illustrated in FIGS. 12A and 12B. The presence of the two pairs ofstacked electrodes 502, 507 allows for creation of a high field regionin higher 506 or a lower 508 plane, thus causing a species of higherdielectric constant to migrate to a higher or lower region respectively.In FIG. 12C, the species of higher dielectric constant is one hemisphere440 of a bichromal sphere, this sphere having a second hemisphere 430 oflower dielectric constant than the hemisphere 440. In FIG. 12D, thespecies of higher dielectric constant is one species 483 of a mixture ofcolored species 483, 484. In both cases, the separation of the speciesgives the effect of differing color states. FIGS. 12C and 12D furtherillustrate the use of shaped material 509, which may be dielectric orconducting materials, to shape the electric fields from the electrodes502, 507.

It will be appreciated that other electronically addressable contrastmedia may readily be substituted for those shown in FIGS. 12A-12D.

It will be appreciated that the present invention need not make use of acolored reflector behind the capsules but may be used to provide backlitdisplays, variable transmission windows and transparent displays;indeed, the present invention may be useful in any application wherelight modulation is desired.

It is appropriate to give some consideration to the problems involved indriving dielectrophoretic displays. The basic physical principles ofdielectrophoresis are discussed below and semi-quantitative predictionsare derived from a simple model. This model also relates physical andelectrical properties of the components of the dielectrophoretic mediumto the strength of the dielectrophoretic force.

An object of charge q in an external electric field Le experiences aforce:F=qE _(e)  (1)The external field does not include the field arising from the chargedobject under consideration (i.e., E_(e)=E−E_(self)), since according toNewton's Laws one cannot pull oneself up by one's own bootstraps. It isadvantageous to express Equation (1) in terms of potentials. Thepotential for force is the potential energy WF=−∇W  (2)and the potential for the electric field is the electrostatic potentialφE _(e)=−∇φ_(e)  (3)Accordingly, Equation (1) above can be re-written as:W=qφ _(e)  (4)

For any general object with a charge density function ρ(r) there areforces beyond the electrophoretic term owing to the distributed natureof the charge distribution. To realize this, it is necessary to begin byrecognizing that the total electrostatic potential energy is simply thesum of all the possible electrostatic energy terms calculated as thesame manner as in Equation (4) above:

$\begin{matrix}{W = {\int_{S}^{\;}{{\rho(r)}{\phi_{e}(r)}\ {\mathbb{d}r}}}} & (5)\end{matrix}$where the integral is over the charge distribution of the object underconsideration. This energy can be broken up into recognizable componentsby expressing the electrostatic potential as a Taylor expansion about asuitable origin:

$\begin{matrix}{{\phi_{e}(r)} = {{\phi_{e}(0)} + {r \cdot {\nabla{\phi_{e}(0)}}} + {\frac{1}{2}{\sum{\sum{r_{i}r_{j}\frac{\partial^{2}\phi}{{\partial r_{i}}{\partial r_{j}}}}}}} + \ldots}} & (6)\end{matrix}$

Substituting Equation (6) into Equation (5) gives:

$\begin{matrix}{W = {{q\;{\phi_{e}(0)}} - {p \cdot {E(0)}} - {\frac{1}{6}{\sum{\sum{Q_{ij}\frac{\partial E_{j}}{\partial r_{i}}(0)}}}} + \ldots}} & (7)\end{matrix}$where q is the electric monopole:

$\begin{matrix}{q = {\int_{S}^{\;}{{\rho(r)}\ {\mathbb{d}r}}}} & (8)\end{matrix}$p is the electric dipole moment:

$\begin{matrix}{p = {\int_{S}^{\;}{{\rho(r)}r\ {\mathbb{d}r}}}} & (9)\end{matrix}$and Q_(ij) represents the components of the electric quadrupole tensor.

Equation (3) is used in the derivation of Equation (7), which shows howthe various moments of the charge distribution interact with the variouselectric field terms. The monopole couples to the electrostaticpotential, the dipole to the field (gradient or first derivative of thepotential), the quadrupole to the field gradient (second derivative ofthe potential) etc. From the expression for electrostatic energy inEquation (7), the forces and torques on charged bodies in an externalfield can be determined. The translational force is determined by takingthe negative gradient of Equation (7). The electrophoretic force is thefirst order term in the Taylor expansion, the dielectrophoretic force isthe second term in the same expansion, and higher order terms representadditional forces which are not relevant for purposes of the presentinvention. The first term of the expansion gives the electrophoreticforce already expressed by Equation (1). The second term is thedielectrophoretic force, F_(DEP), between a dipole and a field gradient:F _(DEP) =p·∇E _(e)  (10)

Thus, a dipole does not feel a force in a uniform electric field, butrather a field gradient is required to exert force a dipole; see FIG.13. In FIG. 13, If the electric field were uniform, the forces F⁻ and F₊on the two parts of the dipole would cancel to give zero net force.Because the two charges that comprise the dipole are at differentpositions and experience different fields, the forces do not completelycancel. The resultant force is the dielectrophoretic force on thedipole. The third term of Equation (7) shows that a quadrupole chargedistribution does not experience a force in a uniform field or in auniform field gradient, but will experience a force due to thederivative of the field gradient.

Equation (10) shows that a dipole experiences a force in the directionof increasing field strength. In other words, dipoles are attracted toregions of high electric field strength. For example, a charged air-gapcapacitor will attract dielectric media, the dielectric media beingpolarized by the electric field in the capacitor gap.

The next step in modeling a dielectrophoretic display is to consider thedielectrophoretic force on a polarizable particle lying within a fluidmedium. The particle typically has no electric dipole except thatinduced by an external field. In such an external field, the particle ispolarized, and has an induced dipole moment that can be acted on by afield gradient. Consider a particle with a complex dielectric constantε*_(p) immersed in a fluid with a complex dielectric constant ε*_(m).Each complex dielectric constant is expressed in terms of the realdielectric constant, a conductivity σ, and the frequency of thesinusoidally varying external field ω:

$\begin{matrix}{ɛ^{*} = {ɛ - {j\frac{\sigma}{\omega}}}} & (11)\end{matrix}$An applied electric field of the form:E=E ₀ e ^(jωt)  (12)polarizes the fluid and the particle. The important parameter whenconsidering dielectrophoresis is the difference between the dipolemoment of the particle and the same volume of the fluid. The excessdipole moment is given by the Clausius-Mosotti relation:p=4πε_(m) a ³ K(ω)E  (13)where ε_(m) is the dielectric constant of the fluid, a the radius of theparticle (assumed to be spherical) and K(ω) is the difference betweenthe complex dielectric constant of the particle (ε*_(p)) and that of thefluid (ε*_(m)), weighted according to the effect of field gathering:

$\begin{matrix}{{K(\omega)} = \frac{ɛ_{p}^{*} - ɛ_{m}^{*}}{ɛ_{p}^{*} + {2\; ɛ_{m}^{*}}}} & (14)\end{matrix}$

The dielectrophoretic force on the particle, using Equation (10) andtaking the real component of a complex quantity, is:F _(DEP) =Re{p·∇E _(e) }=Re{4πε_(m) a ³ K(ω)E·∇E}  (15)This can be transformed to give the time average dielectric force in thesinusoidal external field:F _(DEP)=2πε_(m) a ³ Re{K(ω)}∇(E _(rms))²  (16)where E_(rms) is the root-mean-square electric field strength.

There are two major cases of interest in connection withdielectrophoretic displays, namely that of an insulating particle in aninsulating fluid, and of a conducting particle in an insulating fluid,and these two cases are considered separately below.

A. Insulating Particle in an Insulating Fluid

In principle, all materials act as insulators at sufficiently highfrequencies and as conductors at sufficiently low frequencies. Materialsnormally considered to be insulators may be conductive in the 1 MHzrange, and sometimes at far lower frequencies, while materials normallyconsidered to be conductors may act as insulators at very highfrequencies, perhaps in the MHz or GHz range or above. A cross-overfrequency can be defined as the frequency at which the conductive andnon-conductive components of the complex dielectric function of Equation(11) are equal, and conductive and conductive and insulating regimes canbe defined as follows:Conductive regime: ω<<(π/ε)  (17A)Insulating regime: ω>>(σ/ε)  (17B).

When a (solid) particle is immersed in a fluid, in general thecross-over frequencies of the particle and the fluid will be different,so that there will be a frequency range where one of the particle andthe fluid acts as an insulating dielectric material, whereas the othercomponent acts as a conductor. Within the insulating regime, thecontrast function defined by Equation (11) above can be approximated by:

$\begin{matrix}{{K(\omega)} = \frac{ɛ_{p} - ɛ_{m}}{ɛ_{p} + {2\; ɛ_{m}}}} & (18)\end{matrix}$

From this Equation, it will be seen that if the particle has adielectric constant that exceeds that of the fluid it will be attractedto high-field regions, whereas if the particle has a dielectric constantless than that of the fluid it will be attracted to low-field regions.

FIG. 14 is a graph showing the variation of the contrast function, ascalculated from Equation (18), as a function of ε_(p)/ε_(m). From FIG.14, it will be seen that the contrast function increases monotonicallywith ε_(p)/ε_(m), and is bounded by unity.

B. Conducting Particle in an Insulating Fluid

If, at the applied field frequency, the particle acts as a conductor,the imaginary component of its dielectric constant is much greater thanthe real component, and hence:ε_(p) *≈−jσ/ω  (19).Assuming that the surrounding fluid acts as an insulator, the magnitudeof the particle's dielectric constant far exceeds the magnitude of thefluid's dielectric constant, K(ω) approaches unity, and thedielectrophoretic force is given by:F _(DEP)=2πε_(m) a ³∇(E _(rms))²  (20)

Equation (20) shows that the dielectrophoretic force on a conductingparticle in an insulating fluid always exceeds the dielectrophoreticforce on an insulating particle. To take one practical example, theaforementioned E Ink and MIT patents and applications discloseelectrophoretic media comprising carbon black and titania particles inan insulating hydrocarbon fluid. If such media are operated in adielectrophoretic mode, the dielectrophoretic force on the carbon blackparticles exceeds the dielectrophoretic force on the titania particlesfor otherwise similar conditions.

Finally, a simple model of the dielectrophoretic behavior of anencapsulated electrophoretic medium of the general type shown in FIGS.1-3 will be considered. Inhomogeneities in the electrophoretic layer,for example those due to differences between the fluid and the capsulewalls, induce field gradients. A full analysis of this problem wouldrequire numerical field calculations, but in order to develop a firstapproximation about the magnitude and direction of the field gradientsin such an electrophoretic layer, we consider a very simple model forthe field distribution throughout a capsule by making the approximationthat the electric field divides itself locally between the externalcomponents (the capsule wall and any polymeric binder, which istypically present between the capsules and serves to bind them into amechanically coherent layer) and the internal phase (the fluid and theparticles therein) in the same manner as a vertical stack of thesematerials with no lateral variations in geometry. This crudeapproximation neglects lateral field components and is expected to beparticularly poor near the vertical edges of the capsules, asillustrated in FIGS. 1-3. Using this vertical stack model, the electricfield in the internal phase is given by:

$\begin{matrix}{E_{I\; P} = {\frac{1 + \frac{d_{e}}{d_{I\; P}}}{1 + {\frac{ɛ_{I\; P}^{*}}{ɛ_{e}^{*}}\frac{d_{e}}{d_{I\; P}}}}E_{0}}} & (21)\end{matrix}$where E₀ is the applied voltage, V, divided by the thickness, d, of theelectrophoretic layer, i.e.:E ₀ =V/d  (22)d_(e) is the local thickness of the external phase, d_(IP) is the localthickness of the internal phase, ε_(IP)* and ε_(e)* are the complexdielectric constants of the internal and external phases. In this model,gradients in the electric field within the internal phase arise fromvariations in the local fraction of external phase and the difference indielectric constant or conductivity between the internal and externalphases. Also, gradients in E² are in the plane of the substrates andpoint outwardly (or inwardly) along a capsule's radial direction.Typically, the external phase of an encapsulated electrophoretic mediumis more conductive and has a larger dielectric constant than theinternal phase. In such a medium, the electric field in the internalphase is largest in regions where the capsule is thinnest, which will bealong the lateral perimeter of the capsules (i.e., the left and righthand edges of the capsules as illustrated in FIGS. 1-3), or in the caseof tightly packed capsules, at the surfaces of contact with neighboringcapsules.

Typically, in an encapsulated electrophoretic medium, theelectrophoretic particles have a larger polarizability than the fluid,and so their dielectrophoretic mobility will be positive. The particleswill thus be attracted to the thinnest regions of the capsules along thelateral extremes of the capsules and especially to the vertices of thecapsules.

Consider the application of an alternating voltage to theelectrophoretic medium. The electrophoretic force, F_(ep), acting on theparticles is typically sinusoidal:F _(ep)˜sin ωt  (23)and averages to zero. The dielectrophoretic force, F_(dep), isproportional to the square of the electric field, so its temporalvariation is:F _(dep)˜sin² ωt  (24)which has a non-zero average. Use of a high frequency alternatingvoltage will induce small amplitude oscillations due to theelectrophoretic force and a sinusoidally-modulated but linearly-directedmotion due to the dielectrophoretic force. The total velocity of aparticle is given by the sum of the electrophoretic anddielectrophoretic motions:v=v _(ep) +v _(dep)  (25)where:v _(ep)˜μ_(ep) E ₀ sin ωt  (26)and:v _(dep)˜μ_(dep)∇(E _(rms) ²)sin² ωt  (27)

where μ_(dep) is the dielectrophoretic mobility, which can be derivedfrom Equation (16) and the standard formula for the drag force,F_(drag), on a particle in a viscous fluid:F _(drag)=6πμav  (27A)From Equations (16) and (27A):

$\begin{matrix}{\mu_{dep} = \frac{ɛ_{m}a^{2}{Re}\left\{ {K(\omega)} \right\}}{3\;\mu}} & (28)\end{matrix}$As mentioned above, the time-averaged migration of the particles will betoward the outer lateral edges of the capsules, and especially towardthe vertices of the capsules in this direction.

The timescale for such dielectrophoretic motion can be estimated in thefollowing manner. The gradient in the mean square electric field isapproximately the difference in the mean square field between thecapsule center and the edges, divided by the lateral radius of thecapsule. The field at the center of the capsule is approximately:

$\begin{matrix}{E_{{I\; P},{center}} = {\frac{1 + \frac{H - h_{c}}{h_{c}}}{1 + {\frac{ɛ_{I\; P}^{*}}{ɛ_{e}^{*}}\frac{H - h_{c}}{h_{c}}}}E_{0}}} & (29)\end{matrix}$where H is the ink thickness and h_(c) is the height of the internalphase at capsule center. At the lateral edge of the capsule, thethickness of the internal phase goes to zero and the field at theinternal phase goes to:

$\begin{matrix}{E_{{I\; P},{edge}} = {\frac{ɛ_{e}^{*}}{ɛ_{I\; P}^{*}}E_{0}}} & (30)\end{matrix}$The gradient in the mean square field can be approximated by:

$\begin{matrix}{{\nabla\left( E^{2} \right)} = {\frac{E_{0}^{2}}{a_{c}}\left\lbrack {\left( \frac{1 + \frac{H - h_{c}}{h_{c}}}{1 + {\frac{ɛ_{I\; P}^{*}}{ɛ_{e}^{*}}\frac{H - h_{c}}{h_{c}}}} \right)^{2} - \left( \frac{ɛ_{e}^{*}}{ɛ_{I\; P}^{*}} \right)^{2}} \right\rbrack}} & (31)\end{matrix}$where a_(c) is the lateral radius of the capsule.

It should be noted that since practical encapsulated electrophoreticmedia are composites of several components, the electric field acrossany of the components will be a function of the electrical behavior ofall the other components. For example, over short time scales,differences in dielectric constants between the various components willcause electric field lines to be bent, concentrated, or rarified invarious regions. Over time scales longer than ohmic relaxation times,conductivity variations will determine these effects.

Those skilled in the display art will appreciate that numerous changes,improvements and modifications can be made in the preferred embodimentsof the invention already described without departing from the scope ofthe invention. Accordingly, the whole of the foregoing description isintended to be construed in an illustrative and not in a limitativesense.

1. A display comprising: a substrate having walls defining at least onecavity, the cavity having a viewing surface and a side wall inclined tothe viewing surface; a fluid contained within the cavity; a plurality ofat least one type of electrically charged solid particle within thefluid; and means for applying to the fluid an electric field effectiveto cause movement of the particles to the side wall of the cavity.
 2. Aprocess for operating a display, the process comprising: providing asubstrate having walls defining at least one cavity, the cavity having aviewing surface and a side wall inclined to the viewing surface; a fluidcontained within the cavity; and a plurality of at least one type ofelectrically charged solid particle within the fluid; and applying tothe fluid an electric field effective to cause movement of the solidparticles to the side wall of the cavity.
 3. A display comprising: asubstrate having walls defining at least one cavity, the cavity having aviewing surface and a side wall inclined to the viewing surface; a fluidcontained within the cavity; a plurality of at least one type ofelectrically charged solid particle within the fluid, the solidparticles having a first optical characteristic; a backing memberdisposed on the opposed side of the cavity from the viewing surface, atleast part of the backing member having a second optical characteristicdifferent from the first optical characteristics, the backing memberbeing light-transmissive; and means for applying to the substrate anelectric field effective to cause movement of the solid particles to theside wall of the cavity.
 4. A display according to claim 3 wherein thecavity has a non-circular cross-section as seen from the viewingsurface.
 5. A display according to claim 4 wherein the cavity has apolygonal cross-section as seen from the viewing surface.
 6. A displayaccording to claim 3 having a single type of solid particle formed froman electrically conductive material.
 7. A display according to claim 6wherein the single type of solid particle is formed from a metal orcarbon black.
 8. A display according to claim 3 having a single type ofsolid particle formed from a doped semiconductor.
 9. A display accordingto claim 3 wherein the substrate comprises at least one capsule wall sothat the display comprises at least one capsule.
 10. A display accordingto claim 9 comprising a plurality of capsules, the capsules beingarranged in a single layer.
 11. A display according to claim 3 whereinthe substrate comprises a continuous phase surrounding a plurality ofdiscrete droplets of the fluid having the at least one type of solidparticle therein.
 12. A display according to claim 3 wherein thesubstrate comprises a substantially rigid material having the at leastone cavity formed therein, the substrate further comprising at least onecover member closing the at least one cavity.
 13. A display according toclaim 3 arranged to have light projected on to a surface on the opposedside of the display from the viewing surface.
 14. A process foroperating a display, the process comprising: providing a substratehaving walls defining at least one cavity, the cavity having a viewingsurface and a side wall inclined to the viewing surface, a fluidcontained within the cavity; and a plurality of at least one type ofelectrically charged solid particle within the fluid, the particleshaving a first optical characteristic; and a backing member disposed onthe opposed side of the cavity from the viewing surface, at least partof the backing member having a second optical characteristic differentfrom the first optical characteristic, the backing member beinglight-transmissive; and applying to the substrate an electric fieldeffective to cause movement of the solid particles to the side wall ofthe cavity.
 15. A process according to claim 14 wherein the electricfield is an alternating electric field.
 16. A process according to claim14 having only a single type of solid particle formed from anelectrically conductive material.
 17. A process according to claim 16wherein the electrically conductive material is a metal or carbon black.18. A process according to claim 14 having only a single type of solidparticle formed from a doped semiconductor.
 19. A process according toclaim 14 wherein the substrate comprises at least one capsule wall sothat the display comprises at least one capsule.
 20. A process accordingto claim 19 wherein the substrate comprises a plurality of capsules, thecapsules being arranged in a single layer.
 21. A process according toclaim 14 wherein the substrate comprises a continuous phase surroundinga plurality of discrete droplets of the fluid having the solid particlessuspended therein.
 22. A process according to claim 14 wherein thesubstrate comprises a substantially rigid material having the at leastone cavity formed therein, the substrate further comprising at least onecover member closing the at least one cavity.
 23. A process foroperating a display, the process comprising: providing a substratehaving walls defining at least one cavity, the cavity having a viewingsurface and a side wall inclined to the viewing surface, a fluidcontained within the cavity; and a plurality of solid particles withinthe fluid, the particles having a dielectric constant higher than thedielectric constant of the fluid; and applying to the substrate anon-homogeneous electric field, the electric field being greateradjacent the side wall than in the center of the cavity, thereby causingthe particles to move to the side wall of the cavity.
 24. A process foroperating a display, the process comprising: providing a substratehaving walls defining at least one cavity, the cavity having a viewingsurface and a side wall inclined to the viewing surface, a fluidcontained within the cavity; and a plurality of solid particles withinthe fluid, the particles having a dielectric constant lower than thedielectric constant of the fluid; and applying to the substrate anon-homogeneous electric field, the electric field being smalleradjacent the side wall than in the center of the cavity, thereby causingthe solid particles to move to the side wall of the cavity.
 25. Adisplay comprising: a substrate having walls defining at least onecavity, the cavity having a viewing surface, a rear surface on theopposed side of the cavity from the viewing surface, and a side wallextending between the viewing surface and the rear surface; a fluidcontained within the cavity; a plurality of at least one type ofelectrically charged solid particle within the fluid; a front electrodeadjacent the viewing surface of the cavity; a rear electrode adjacentthe rear surface; and a side electrode adjacent the side wall, thedisplay having a first optical state in which the solid particles lieadjacent the front electrode, a second optical state in which the solidparticles lie adjacent the rear electrode and a third optical state inwhich the solid particles lie adjacent the side electrode.
 26. A displaycomprising: a substrate having walls defining at least one cavity, thecavity having a viewing surface, a rear surface on the opposed side ofthe cavity from the viewing surface, and a side wall extending betweenthe viewing surface and the rear surface; a fluid contained within thecavity; a plurality of at least one type of electrically charged solidparticle within the fluid; a front electrode adjacent the viewingsurface of the cavity; a rear electrode adjacent the rear surface; and aside electrode adjacent the side wall, the display having a firstoptical state in which the solid particles lie adjacent the viewingsurface, a second optical state in which the solid particles lieadjacent the rear surface and a third optical state in which the solidparticles lie adjacent the side wall.